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Properties

Label 1672.2.a
Level $1672$
Weight $2$
Character orbit 1672.a
Rep. character $\chi_{1672}(1,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $11$
Sturm bound $480$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1672 = 2^{3} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1672.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(480\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1672))\).

Total New Old
Modular forms 248 44 204
Cusp forms 233 44 189
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(11\)\(19\)FrickeDim
\(+\)\(+\)\(+\)$+$\(4\)
\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(-\)\(+\)$-$\(9\)
\(+\)\(-\)\(-\)$+$\(4\)
\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(-\)$+$\(6\)
\(-\)\(-\)\(+\)$+$\(6\)
\(-\)\(-\)\(-\)$-$\(6\)
Plus space\(+\)\(20\)
Minus space\(-\)\(24\)

Trace form

\( 44 q + 32 q^{9} + O(q^{10}) \) \( 44 q + 32 q^{9} + 6 q^{11} - 4 q^{13} + 12 q^{15} + 4 q^{17} + 16 q^{21} + 36 q^{25} - 12 q^{27} + 20 q^{29} - 24 q^{35} + 28 q^{37} - 12 q^{39} - 12 q^{41} - 16 q^{43} + 44 q^{45} + 12 q^{49} - 40 q^{51} - 8 q^{59} - 4 q^{61} - 12 q^{63} - 8 q^{65} - 40 q^{67} + 28 q^{69} - 4 q^{73} - 28 q^{75} - 8 q^{77} + 12 q^{81} - 24 q^{83} - 16 q^{85} - 12 q^{87} + 20 q^{89} - 48 q^{91} - 12 q^{93} - 44 q^{97} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1672))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11 19
1672.2.a.a 1672.a 1.a $1$ $13.351$ \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}-3q^{9}-q^{11}+2q^{13}+\cdots\)
1672.2.a.b 1672.a 1.a $1$ $13.351$ \(\Q\) None \(0\) \(1\) \(-3\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+2q^{7}-2q^{9}-q^{11}+\cdots\)
1672.2.a.c 1672.a 1.a $1$ $13.351$ \(\Q\) None \(0\) \(1\) \(2\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-3q^{7}-2q^{9}-q^{11}+\cdots\)
1672.2.a.d 1672.a 1.a $2$ $13.351$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(-1\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-\beta q^{5}+(1-\beta )q^{7}+\beta q^{9}-q^{11}+\cdots\)
1672.2.a.e 1672.a 1.a $3$ $13.351$ 3.3.229.1 None \(0\) \(0\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+(1+\beta _{1})q^{7}+\beta _{2}q^{9}+\cdots\)
1672.2.a.f 1672.a 1.a $4$ $13.351$ 4.4.13676.1 None \(0\) \(-1\) \(-3\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1672.2.a.g 1672.a 1.a $5$ $13.351$ 5.5.3979184.1 None \(0\) \(1\) \(7\) \(8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{3}+(1+\beta _{1})q^{5}+(2-\beta _{1})q^{7}+\cdots\)
1672.2.a.h 1672.a 1.a $6$ $13.351$ 6.6.57500224.1 None \(0\) \(-4\) \(-4\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1672.2.a.i 1672.a 1.a $6$ $13.351$ 6.6.106392688.1 None \(0\) \(-4\) \(-3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{5})q^{5}-\beta _{5}q^{7}+\cdots\)
1672.2.a.j 1672.a 1.a $6$ $13.351$ 6.6.576096652.1 None \(0\) \(4\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+\beta _{4}q^{5}+\beta _{3}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1672.2.a.k 1672.a 1.a $9$ $13.351$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(1\) \(6\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{7})q^{5}+\beta _{8}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1672))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1672)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(418))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(836))\)\(^{\oplus 2}\)